Average Error: 0.1 → 0.1
Time: 3.8s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + \left(y \cdot \left(2 \cdot \log \left({z}^{\frac{1}{3}}\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + \left(y \cdot \left(2 \cdot \log \left({z}^{\frac{1}{3}}\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)
double code(double x, double y, double z) {
	return ((double) (((double) (x * 0.5)) + ((double) (y * ((double) (((double) (1.0 - z)) + ((double) log(z))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x * 0.5)) + ((double) (((double) (1.0 - z)) * y)))) + ((double) (((double) (y * ((double) (2.0 * ((double) log(((double) pow(z, 0.3333333333333333)))))))) + ((double) (y * ((double) log(((double) cbrt(z))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1 - z\right) + y \cdot \log z\right)}\]

  4. Applied associate-+r+0.1

    \[\leadsto \color{blue}{\left(x \cdot 0.5 + y \cdot \left(1 - z\right)\right) + y \cdot \log z}\]

  5. Simplified0.1

    \[\leadsto \color{blue}{\left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right)} + y \cdot \log z\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.1

    \[\leadsto \left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + y \cdot \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\]

  8. Applied log-prod0.1

    \[\leadsto \left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + y \cdot \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\]

  9. Applied distribute-lft-in0.1

    \[\leadsto \left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + \color{blue}{\left(y \cdot \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)}\]

  10. Simplified0.1

    \[\leadsto \left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + \left(\color{blue}{y \cdot \left(2 \cdot \log \left(\sqrt[3]{z}\right)\right)} + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]
  11. Using strategy rm

  12. Applied pow1/30.1

    \[\leadsto \left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + \left(y \cdot \left(2 \cdot \log \color{blue}{\left({z}^{\frac{1}{3}}\right)}\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]

  13. Final simplification0.1

    \[\leadsto \left(x \cdot 0.5 + \left(1 - z\right) \cdot y\right) + \left(y \cdot \left(2 \cdot \log \left({z}^{\frac{1}{3}}\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))